IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i16p2884-d886242.html
   My bibliography  Save this article

A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing

Author

Listed:
  • Ibrahim Mohammed Sulaiman

    (Institute of Strategic Industrial Decision Modelling (ISIDM), School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Sintok 06010, Malaysia)

  • Aliyu Muhammed Awwal

    (Department of Mathematics, Faculty of Science, Gombe State University (GSU), Gombe 760214, Nigeria
    GSU-Mathematics for Innovative Research Group, Gombe Srare University (GSU), Gombe 760214, Nigeria)

  • Maulana Malik

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia (UI), Depok 16424, Indonesia)

  • Nuttapol Pakkaranang

    (Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand)

  • Bancha Panyanak

    (Research Group in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

Nonlinear systems of equations are widely used in science and engineering and, therefore, exploring efficient ways to solve them is paramount. In this paper, a new derivative-free approach for solving a nonlinear system of equations with convex constraints is proposed. The search direction of the proposed method is derived based on a modified conjugate gradient method, in such a way that it is sufficiently descent. It is worth noting that, unlike many existing methods that require a monotonicity assumption to prove the convergence result, our new method needs the underlying function to be pseudomonotone, which is a weaker assumption. The performance of the proposed algorithm is demonstrated on a set of some test problems and applications arising from compressive sensing. The obtained results confirm that the proposed method is effective compared to some existing algorithms in the literature.

Suggested Citation

  • Ibrahim Mohammed Sulaiman & Aliyu Muhammed Awwal & Maulana Malik & Nuttapol Pakkaranang & Bancha Panyanak, 2022. "A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing," Mathematics, MDPI, vol. 10(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2884-:d:886242
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/16/2884/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/16/2884/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anton Rodomanov & Yurii Nesterov, 2021. "New Results on Superlinear Convergence of Classical Quasi-Newton Methods," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 744-769, March.
    2. Awwal, Aliyu Muhammed & Kumam, Poom & Abubakar, Auwal Bala, 2019. "Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Mohammed Yusuf Waziri & Jamilu Sabi’u, 2015. "A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-8, September.
    4. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dandan Li & Yong Li & Songhua Wang, 2024. "An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications," Mathematics, MDPI, vol. 12(16), pages 1-22, August.
    2. Aliyu Yusuf & Nibron Haggai Manjak & Maggie Aphane, 2024. "A Modified Three-Term Conjugate Descent Derivative-Free Method for Constrained Nonlinear Monotone Equations and Signal Reconstruction Problems," Mathematics, MDPI, vol. 12(11), pages 1-21, May.
    3. Rabiu Bashir Yunus & Nooraini Zainuddin & Hanita Daud & Ramani Kannan & Samsul Ariffin Abdul Karim & Mahmoud Muhammad Yahaya, 2023. "A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rabiu Bashir Yunus & Nooraini Zainuddin & Hanita Daud & Ramani Kannan & Samsul Ariffin Abdul Karim & Mahmoud Muhammad Yahaya, 2023. "A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control," Mathematics, MDPI, vol. 11(14), pages 1-17, July.
    2. Awwal, Aliyu Muhammed & Kumam, Poom & Abubakar, Auwal Bala, 2019. "Spectral modified Polak–Ribiére–Polyak projection conjugate gradient method for solving monotone systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    3. Mrad, Hatem & Fakhari, Seyyed Mojtaba, 2024. "Optimization of unconstrained problems using a developed algorithm of spectral conjugate gradient method calculation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 282-290.
    4. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram & Ravina Sharma, 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems," Mathematics, MDPI, vol. 11(23), pages 1-14, December.
    5. Zhen-Yuan Ji & Yu-Hong Dai, 2023. "Greedy PSB methods with explicit superlinear convergence," Computational Optimization and Applications, Springer, vol. 85(3), pages 753-786, July.
    6. Waziri, Mohammed Yusuf & Ahmed, Kabiru & Sabi’u, Jamilu, 2019. "A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 645-660.
    7. Siti Farhana Husin & Mustafa Mamat & Mohd Asrul Hery Ibrahim & Mohd Rivaie, 2020. "An Efficient Three-Term Iterative Method for Estimating Linear Approximation Models in Regression Analysis," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
    8. Vladimir Krutikov & Elena Tovbis & Predrag Stanimirović & Lev Kazakovtsev, 2023. "On the Convergence Rate of Quasi-Newton Methods on Strongly Convex Functions with Lipschitz Gradient," Mathematics, MDPI, vol. 11(23), pages 1-15, November.
    9. Halilu, Abubakar Sani & Majumder, Arunava & Waziri, Mohammed Yusuf & Ahmed, Kabiru, 2021. "Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 520-539.
    10. Elena Tovbis & Vladimir Krutikov & Lev Kazakovtsev, 2024. "Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction," Mathematics, MDPI, vol. 12(11), pages 1-27, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2884-:d:886242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.